How do you simplify $(5+ sqrt 5)/(8- sqrt 5)$ ?

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Answer 1 · 2016-02-16T11:46:08

By multiply numerator and denominator by denominator's conjugate pair. Solution is $(45+13√5)/(59)$

To simplify $(5+√5)/(8−√5)$ , one has to multiply numerator and denominator by denominator's conjugate pair which is $(8+√5)$ .

Hence, $(5+√5)/(8−√5)$ becomes

$((5+√5)(8+√5))/((8−√5)(8+√5))$ i.e.

$(40+5√5+8√5+5)/(64−5)$ i.e.

$(45+13√5)/(59)$

How do you simplify (5+ sqrt 5)/(8- sqrt 5)(5+ sqrt 5)/(8- sqrt 5)?